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Adaptive robust control of nonholonomic systems with stochastic disturbances. (English) Zbl 1117.93027
Summary: This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances. The objective is to design the almost global adaptive asymptotical controllers in probability u 0 and u 1 for the systems by using discontinuous control. A switching control law u 0 is designed to almost globally asymptotically stabilize the state x 0 in both the singular x 0 (t 0 )=0 case and the non-singular x 0 (t 0 )0 case. Then the state scaling technique is introduced for the discontinuous feedback into the (x 1 ,x 2 ,,x n )-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law u 1 has been presented for (x 1 ,x 2 ,,x n )-subsystem for both different u 0 in non-singular x 0 (t 0 )0 case and the singular case x 0 (t 0 )=0. The control algorithm validity is proved by simulation.
93B35Sensitivity (robustness) of control systems
93C42Fuzzy control systems
93E03General theory of stochastic systems
93E15Stochastic stability
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